Question
Find Greatest Common Divisor of 287 and 2009, using prime factorization.
Answer
The GCD of given numbers is 287.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}287 =& 7\cdot41\\[8pt]2009 =& 7\cdot7\cdot41\\[8pt]\end{aligned}$$(view steps on how to factor 287 and 2009. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}287 =& \color{blue}{\boxed{7}}\cdot\color{red}{\boxed{41}}\\[8pt]2009 =& \color{blue}{\boxed{7}}\cdot7\cdot\color{red}{\boxed{41}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 7\cdot41 = 287 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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